Volume Three of
Essays In Cosmic Archaeology
Essays where anthropological cosmology
meet with cosmology in physics
Genesis Project California 2021!
⋅
⋅
© 2021 By Ian Beardsley"
ALL RIGHTS RESERVED INCLUDING THE RIGHT OF REPRODUCTION IN WHOLE OR IN
PART IN ANY FORM. PUBLISHED BY GENESIS PROJECT
of 1 9
The Fundamental AiBioequations
Ian Beardsley (September 23, 2021)!
Physics, University of Oregon
Genesis Project California 2021
⋅
⋅
of 2 9
1. Silicon and Carbon
We guess that artificial intelligence (AI) has the golden ratio, or its conjugate in its means
geometric, harmonic, and arithmetic by molar mass by taking these means between doping
agents phosphorus (P) and boron (B) divided by semiconductor material silicon (Si) :
Which can be written
We see that the biological elements, H, N, C, O compared to the AI elements P, B, Si is the
golden ratio conjugate (phi) as well:
So we can now establish the connection between artificial intelligence and biological life:
Which can be written:
Where HNCO is isocyanic acid, the most basic organic compound. We write in the arithmetic
mean:
PB
Si
=
(30.97)(10.81)
28.09
= 0.65
2 PB
P + B
1
Si
=
2(30.97)(10.81)
30.97 + 10.81
1
28.09
= 0.57
0.65 + 0.57
2
= 0.61 ≈ ϕ
PB(P + B) + 2PB
2(P + B)Si
≈ ϕ
C + N + O + H
P + B + Si
≈ ϕ
(P + B + Si)
PB(P + B) + 2PB
2(P + B)Si
≈ (C + N + O + H )
PB
[
P
Si
+
B
Si
+ 1
]
+
2 PB
P + B
[
P
Si
+
B
Si
+ 1
]
≈ 2HCNO
[
PB +
2 PB
P + B
+
P + B
2
][
P
Si
+
B
Si
+ 1
]
≈ 3HNCO
of 3 9
Which is nice because we can write in the second first generation semiconductor as well
(germanium) and the doping agents gallium (Ga) and arsenic (As):
Where
Where ZnSe is zinc selenide, an intrinsic semiconductor used in AI, meaning it doesn’t require
doping agents. We now have:
2. Germanium And Carbon
We could begin with semiconductor germanium (Ge) and doping agents gallium (Ga) and
Phosphorus (P) and we get a similar equation:
,
In grams per mole. Then we compare these molar masses to the molar masses of the
semiconductor material Ge:
Then, take the arithmetic mean between these:
We then notice this is about the golden ratio conjugate, , which is the inverse of the golden
ratio, . . Thus, we have
[
PB +
2 PB
P + B
+
P + B
2
][
P
Si
+
B
Si
+ 1
]
≈ HNCO
[
Ga
Ge
+
As
Ge
+ 1
]
Zn
Se
≈
[
P
Si
+
B
Si
+ 1
]
[
Ga
Ge
+
As
Ge
+ 1
]
PB
(
Zn
Se
)
+
2 PB
P + B
(
Zn
Se
)
+
P + B
2
(
Zn
Se
)
≈ HNCO
2GaP
Ga + P
= 42.866
GaP = 46.46749
2GaP
Ga + P
1
Ge
=
42.866
72.61
= 0.59
GaP
1
Ge
=
46.46749
72.61
= 0.64
0.59 + 0.64
2
= 0.615
ϕ
Φ
ϕ ≈
1
Φ
of 4 9
1.
2.
This is considering the elements of artificial intelligence (AI) Ga, P, Ge, Si. Since we want to find
the connection of artificial intelligence to biological life, we compare these to the biological
elements most abundant by mass carbon (C), hydrogen (H), nitrogen (N), oxygen (O),
phosphorus (P), sulfur (S). We write these CHNOPS (C+H+N+O+P+S) and find:
A similar thing can be done with germanium, Ge, and gallium, Ga, and arsenic, As, this time
using CHNOPS the most abundant biological elements by mass:
We can also make a construct for silicon doped with gallium and phosphorus:
GaP(Ga + P) + 2GaP
2(Ga + P)Ge
≈ ϕ
GaP(Ga + P) + 2GaP
2(Ga + P)Si
≈ Φ
CHNOPS
Ga + As + Ge
≈
1
2
[
Ga As +
2Ga As
Ga + As
+
Ga + As
2
][
Ga
Ge
+
As
Ge
+ 1
]
≈ CHNOPS
[
Ga
Si
+
As
Si
+ 1
]
Ga As
(
O
S
)
+
2Ga As
Ga + As
(
O
S
)
+
Ga + As
2
(
O
S
)
≈ CHNOPS
O
S
≈
[
Ga
Ge
+
As
Ge
+ 1
]
[
Ga
Si
+
As
Si
+ 1
]
Ga As(G a + A s) + 2Ga As
2(Ga + As)Ge
≈ 1
C + H + N + O + P + S
Ga + As + Ge
≈
1
2
(C + N + O + H ) ≈
2(Ga + P)Si
GaP(Ga + P) + 2GaP
(P + B + Si)
HNCO ≈
2(Ga + P)Si
(Ga + P)
[
GaP +
2GaP
Ga + P
]
(P + B + Si)
of 5 9
And for germanium doped with gallium and phosphorus:
Here is a table of the AI biological equations…
HNCO ≈
2(P + B + Si)Si
GaP +
2GaP
Ga + P
GaP(Ga + P) + 2GaP
2(Ga + P)Ge
≈ ϕ
[
GaP +
2GaP
Ga + P
+
Ga + P
2
][
P
Ge
+
B
Ge
+
Si
Ge
]
≈ HNCO
[
Ga
Ge
+
As
Ge
+ 1
]
GaP
(
B
S
)
+
2GaP
Ga + P
(
B
S
)
+
Ga + P
2
(
B
S
)
≈ HNCO
of 6 9
The Fundamental AI Bioequations
[
PB +
2 PB
P + B
+
P + B
2
][
P
Si
+
B
Si
+ 1
]
≈ HNCO
[
Ga
Ge
+
As
Ge
+ 1
]
[
Ga As +
2Ga As
Ga + As
+
Ga + As
2
][
Ga
Ge
+
As
Ge
+ 1
]
≈ CHNOPS
[
Ga
Si
+
As
Si
+ 1
]
[
GaP +
2GaP
Ga + P
+
Ga + P
2
][
P
Ge
+
B
Ge
+
Si
Ge
]
≈ HNCO
[
Ga
Ge
+
As
Ge
+ 1
]
HNCO ≈
2(P + B + Si)Si
GaP +
2GaP
Ga + P
PB(P + B) + 2PB
2(P + B)Si
≈ ϕ
Ga As(G a + A s) + 2Ga As
2(Ga + As)Ge
≈ 1
GaP(Ga + P) + 2GaP
2(Ga + P)Ge
≈ ϕ
GaP(Ga + P) + 2GaP
2(Ga + P)Si
≈ Φ
C + N + O + H
P + B + Si
≈ ϕ
C + H + N + O + P + S
Ga + As + Ge
≈
1
2
Zn
Se
≈
[
P
Si
+
B
Si
+ 1
]
[
Ga
Ge
+
As
Ge
+ 1
]
O
S
≈
[
Ga
Ge
+
As
Ge
+ 1
]
[
Ga
Si
+
As
Si
+ 1
]
of 7 9
3. Using The Fundamental Equations
Now that we have outlined the fundamental AI Bioequations, let us put them to use. We
consider:
Making the approximations: ,
, we obtain:
Which can further be written by saying :
Which is interesting because the Si times itself is then equal to something times itself in that Ge
and Si are both semiconducting materials, but Ge is larger than Si, however this is compensated
for by reducing it by a factor of the golden ratio conjugate, phi. The equation is however only
79% accurate because there has been a lot of drift due to so many approximations. However if
we reduce phi by a factor of itself and write:
It is then 99% accurate:
If we do the same with the other and write:
(P + B + Si )
PB(P + B) + 2PB
2(P + B)Si
≈ (C + N + O + H )
HNCO ≈
2(P + B + Si )Si
GaP +
2GaP
Ga + P
GaP ≈ ϕGe
2GaP
Ga + P
≈ ϕGe
PB ≈ ϕSi
2Si
2
Ge
= ϕSi +
2P B
P + B
2P B
P + B
≈ ϕSi
Si
2
= ϕGeSi
Si
2
= ϕ
2
GeSi
28.09 = (72.64)(28.09)(0.381924) = 27.9g/mol
27.916
28.09
= 0.99
2Si
2
Ge
= ϕ
2
Si +
2P B
P + B
of 8 9
We have:
Which is better but still only 81% accurate. However if we write it:
Then it is 95.87% accurate. But we see in the first approximation that . That is we
have boron, the element that is out of place in the AI periodic table resulting in the dynamics of
our equations. So, we can write…
This gives…
Which is 26.836 which is close to aluminum (Al=26.98) which is the dummy representative for
boron in our equations. We have incredibly:
With an accuracy of nearly 100%. This becomes…
While phosphorus, boron, silicon, and germanium and gallium and arsenic are the primary AI
elements, gold (Au), Silver (Ag) and copper (Cu), are the fundamental AI elements in that they
conductive, ductile, and malleable. Incredibly, the number 3 in the above equation is the ratio of
gold to copper in molar mass, so we have…
21.72 = (0.381924)(28.09) + 16.026 = 10.72 + 16.026 = 26.75
2Si
2
Ge
= ϕ
3
Si +
2P B
P + B
phi
2
Si ≈ B
2Si
2
Ge
= B +
2P B
P + B
10.81 + 16.02 = B +
2P B
P + B
Al = B +
2P B
P + B
Al = B
3P + B
P + B
Al = B
Au
Cu
P + B
P + B
Au
Cu
=
196.97
63.55
= 3.099 ≈ 3
of 9 9
The Author
of 1 10
Planetary Frequencies And The Asteroids
Ian Beardsley (September 22, 2021)!
Physics, University of Oregon
Genesis Project California 2021
⋅
⋅
of 2 10
Abstract
In an effort to see if the frequencies of the orbits of a planets has an effect on the asteroids in
the asteroid belt, the interior planets are considered and considered to have the greatest effect
when the three planets interior to the asteroid belt, the terrestrial planets, are all aligned and on
the same side of the sun."
1. Planetary Frequency
Asteroids:"
"
1AU=1.496E11m"
(2.7) (1.496E11)=4.0392E11m"
Mars:"
R4=(1.52)(1.496E11)=2.274E11m"
Earth:"
R3=1.496E11m"
Venus:"
R2=(0.72)(1.496E11)=1.1E11m"
The force is calculated for mars acting on an asteroid of 2,200 kg which is the minimum size
(0.5m in radius) a meteor needs to be to make it to the earth surface without burning up. That
is, to become a meteorite. (See Figure 1)"
Mars"
R5-R4=1.7652E11m "
"
"
Mars year is 687 days"
(687)(24)(60)(60)=59356800 seconds"
P=0.072 Watts"
R
5
=
2.2AU + 3.2AU
2
= 2.7AU
F = G
Mm
r
2
= (6.67408E − 11)
(2,200kg)(6.39E 24kg)
(1.7652E11m)
2
= 3.01E − 6N
2π (R
4
)(3.01E − 6N ) = 4.30E6J
of 3 10
Earth!
R3=1.496E11m!
F=1.3557E-5N!
W=1.2743E7J!
The earth year is 365 days!
(365)(24)(60)(60)=31536000 seconds!
P=0.404 Watts!
Venus!
R2=1.1E11m!
F=8.272E-6N!
W=5.717E6J!
Venus year is 225 days!
(225)(24)(60)(60)=19440000 seconds!
P=0.294 Watts!
2. The Work Done
Taking the sum of our energies for all three planets we have!
4.30E6J+1.2743E7J+5.717E6J=2.276E7!
The work done for the Earth to move and asteroid of our 2,200kg is:!
!
=5E6 Joules!
Using mass of Earth as 5.972E24kg!
The work in moving an asteroidal meteor of 2,200kg from the asteroid belt to Earth by Earth
gravity due to its mass of 5.972E24kg is 5E6 Joules. We derived a total due to Venus, Earth,
and Mars acting on the asteroid belt over their respective orbits of one revolution each of
2.276E7 Joules."
W(r) = − GMm
(
1
R
5
−
1
R
3
)
of 4 10
!
Figure 1: Planets operate on asteroids.
of 5 10
3. Planetary Cycles
We want to to start with Venus, Earth, and Mars aligned in a straight line on the same side of
the sun and, to do this and visualize things we will approximate for two revolutions of Venus we
have one revolution of Earth, and one third revolution of Mars.!
1. As Venus does one revolution, Earth goes to 180 degrees, and
Mars goes to 120 degrees.!
!
2. Now, at the second revolution of Venus, Earth and Venus are
aligned on one side of the Sun, and Mars is 2/3 the way around its
orbit or at 240 degrees.!
!
3. Now, on the third revolution of Venus, Mars and Venus are aligned
on the same side of the sun and the earth is aligned with these on
the opposite side.!
!
4. Now, at the fourth revolution of Venus, the Earth is at zero
degrees and Mars is at 120 degrees again, but now Venus and
the Earth are aligned on the same side of the Sun.!
of 6 10
!
5. Now at the fifth revolution of Venus the Earth is at 180
degrees in alignment with Venus, but on the opposite side of the
Sun and Mars is at 240 degrees.!
!
6. Now at the sixth orbit of Venus alignment between all three
occurs on the same side of the sun.!
Venus Year: 224.70 days!
Earth Year: 365.26 days!
Mars Year: 685.98 days!
We see in this estimate of 1 Earth is 2 Venus’, Mars swings between 120 degrees and 240
degrees is!
!
!
Is approximately in the golden ratio conjugate: !
!
120
360
= 0.33333 ≈ = (1 − ϕ)
240
360
= 0.66667 ≈ ϕ
ϕ =
5 − 1
2
= 0.618...
of 7 10
As Mars swings between these it puts the Earth and Mars in alignment. After 6 cycles of Venus
all three planets are aligned on the same side of the sun. This is all done in terms of the Venus
year. Venus is like the ground state of an electron in an atom. We can say “El base es el fondo”
to quote the Mexican artist Flash Romozi. However we see there is an accrued error after six
cycles that puts Earth in Mars position of a little better than 240 degrees with Venus and Mars
at close to zero degrees. (Figure 2)!
After 3 revolutions of Venus when the planets are all aligned, but not all on the same side of the
sun, the accrued error for Earth puts it closer to 0 degrees than with 6 revolutions and is at
304.392 degrees. We obtain this as follows…!
3(221.464)=664.392!
664.392/360=1.845533333!
0.845533333(360)=304.392!
This gives us a difference between Earth after six revolutions and Earth after 3 revolutions of!
304.392-248.76=55.632 degrees!
Figure 2: Earth in Mars 240 position!
of 8 10
We see 1 Mars equals 3 Venus’ is a good estimate (3.05732) but 1 Earth equals 2 Venus is a
bad one. It is actually close to the golden ratio ( ). The ratio between Venus and
Earth is:!
!
With !
It is easy for Venus and Mars to align:!
!
This is because with the former in and being irrational due to the square root of five, it
cannot be written as a fraction between two integers, which means in the decimal it never
repeats with regularity but rather has no pattern. This is why Nature uses the golden ratio for
closest packing (i.e. you can organize components of a structure with it without them
interfering with one another).!
4. The Mass of the Asteroid
Now we sum up the Power in watts that we calculated earlier:!
0.294J/s+0.404J/s+0.072J/s=0.77J/s!
We multiply this by the number of seconds in our six revolutions of Venus, which is 116484480
seconds, and get 89693049.6 Joules = 8.96E7J. We computed the work for Earth to move an
asteroidal meteor of 2,200kg from the asteroid belt to itself is 5E6 Joules. The 2,200kg meteor
(0.5 meter in radius) is the minimum mass for a meteor to make it to the surface of the earth
before burning up, so it can be found and studied as a meteorite. But our figure of 8.96E7J can
will bring in a larger meteor. Just how large and massive is it? We have:!
!
!
The density of a nickel-iron meteor is 4200 kg/m3. This means it is 9.27 cubic meters in
volume, which is 1.30 meters in radius, or 2.6 meters across. It is a little better than twice as
large. Asteroids larger than 35 meters across can pose a threat to a city or town on the order of
a nuclear detonation.!
5. Discussion
Venus was important to the Mayans. It represented Quetzalcoatl, called Kukulcan by them, and
was the most important God to them, the sky God. They tracked its positions in their books,
called codices and timed their ceremonies by them. It seems the architecture of their city
Uxmal in Yucatan was designed with Venus in mind and Yucatan is where it is believed an
asteroid landed that brought about the extinction of the dinosaurs. It is believed it made the
Φ = 1.618
224.70
365/26
= 0.615
0.615 ≈ 0.618 = ϕ
686.98
224.70
= 3.057 ≈ 3
ϕ
ϕ
8.96E 7J = − GM
e
M
A
(
1
R
5
−
1
R
3
)
M
A
= 38940.956kg = 3.894E4kg
of 9 10
180km wide impact crater, Chicxulub. While Venus has a year of 225 days, it moves across the
sky with an oscillating cycle of 584 days. Five of these cycles is 2,920 days which is eight
Suns. It is believed this was important to the Maya who did not have place significant numerics
and represented everything in the ratios of whole numbers, like 5 Venus’ is 8 Suns.
Quetzalcoatl was also the God of war, and if we have noticed one thing the planet Mars is in
phase with Venus. Mars was the Roman God of war.!
6. Conclusion
The average size of a meteor as adopted by the IAU in 2017 is 30 micrometers to 1 meter in
diameter. The small meteors are usually the size of a grain of sand, or a small pebble and these
burn up before coming to the ground. The illumination we see when we see a shooting star is
due to the atmosphere emitting light because it is heated due to friction from the meteor at
high velocities (10-70 km/s on average). If the meteor is to make it to the ground thus
becoming a meteorite, it must be at least one meter in diameter. Typically less than 5% make it
to the ground. Our method here due to the planets pulling a meteor out of the asteroid belt can
pull one out of a little better than twice this size. Meteors can be as large as 100 meters in
diameter. Anything larger than this is considered an asteroid. Asteroidal meteors are meteors
that come from the asteroid belt, called meteoroids. !
of 10 10
The Author!
of 1 18
Five-fold Symmetry in AI
Ian Beardsley (Sept 22, 2021)!
Physics, University of Oregon
Genesis Project California 2021
⋅
⋅
of 2 18
Abstract
We show that the artificial intelligence elements take the form of mathematical theorems,
suggesting that AI can be taken as a mathematical construct in the physical nature of the
elements from which it is made.!
1. Introduction!
To make artificial intelligence (AI) we need semiconductors, like diodes and transistors. To
make semi conductors we need to dope Silicon Si 4- with a group 13 doping agent to have
positive silicon such as with boron B 3- or with a group 15 doping agent like phosphorus P 5-
to have negative type silicon. Or we can dope germanium Ge 4- with a group 13 doping agent
like gallium Ga 3- for positive type germanium or with a group 15 doping agent like arsenic As
5- to have negative type silicon. We connect the negative with the positive to have a
semiconductor, meaning a current can run through it in only one direction. !
We pull these AI elements out of the periodic table of the elements to make an AI periodic
table:!
We now notice we can make a 3 by 3 matrix of it, which lends itself to to the curl of a vector
field, by including biological elements carbon C (above Si):!
=!
=!
=!
!
i
j
k
∂
∂x
∂
∂y
∂
∂z
(C ⋅ P)y (Si ⋅ G a)z (Ge ⋅ As)y
(Ge ⋅ As − Si ⋅ Ga)
i + (C ⋅ P)
k
[
(72.64)(74.92) − (28.09)(69.72)
]
i +
[
(12.01)(30.97)
]
k
3,482
(
g
mol
)
2
i + 372
(
g
mol
)
2
k
of 3 18
Let us dot this with and take the double integral over Si to Ge over
both variable sets:!
=!
=!
=!
=!
!
!
Now let us take the harmonic mean between Si and Ge. It is!
!
And the arithmetic mean between them:!
!
We see the value of 44.3 g/mol is somewhere between the harmonic and arithmetic mean.
Perhaps it is the geometric mean…!
!
Thus we can say…!
(
zd ydz
i + yd xdy
k
)
∫
Ge
Si
∫
Ge
Si
(
3,483
(
g
mol
)
2
i + 372
(
g
mol
)
2
k
)
⋅
(
zd ydz
i + yd xdy
k
)
∫
Ge
Si
∫
Ge
Si
(
3,483
(
g
mol
)
2
⋅ zdzd y + 372
(
g
mol
)
2
⋅ yd x d y
)
∫
Ge
Si
3,483
(
(72.64 − 28.09)
2
2
)
dy +
∫
Ge
Si
372y ⋅ (72.64 − 28.09)dy
3456359
(
g
mol
)
4
(72.64 − 28.09) + 16573
(
g
mol
)
3
(
(72.64 − 28.09)
2
2
)
170427030.8
(
g
mol
)
5
5
170427030.8 = 44.3g /m ol
2SiGe
Si + Ge
= 40.5g/mol
Si + Ge
2
= 50.365g/mol
SiGe = 45g/mol
of 4 18
!
!
Which like Stoke’s Theorem in that it relates an integral of a flux over a surface to path integral.
The expression on the right-hand side of the equation is the geometric mean between Si and
Ge. This integral can better be represented with product calculus:!
!
Where and and n=2. If we we say the arithmetic mean is A, and the harmonic
mean is H, the geometric mean G…!
!
This is!
!
This is quite interesting because!
!
!
!
I say interesting because we can write all three of these as one equation, the f-mean:!
!
The harmonic mean and the arithmetic mean are special cases of the power-mean which is the
case when , the harmonic mean when p=-1, and the arithmetic mean when p=1.!
u = (CP ⋅ y, SiGa ⋅ z, G a As ⋅ y)
5
∫
Ge
Si
∫
Ge
Si
∇ ×
u ⋅ d
a = ex p
(
1
Ge − Si
∫
Ge
Si
ln(x)d x
)
5
∫
Ge
Si
∫
Ge
Si
∇ ×
u ⋅ d
a =
n
n
∏
i=1
x
i
x
1
= Si
x
2
= Ge
A + H
2
= 45.4325 ≈ G
Si
2
+ 6SiGe + Ge
2
4(Si + Ge)
≈ SiGe
H(a, b) =
1
1
b − a
∫
b
a
dx
x
A(a, b) =
1
b − a
∫
b
a
xd x
G(a, b) = ex p
(
1
Ge − Si
∫
b
a
ln(x)d x
)
M
f
(x
1
, …x
n
) = f
−1
(
1
n
n
∑
i=1
f (x
i
)
)
f (x) = x
p
of 5 18
But what is interesting to me is that to get the geometric mean from the f-mean we have to
change the function f(x) to f(x)=ln(x). This is when it becomes simpler to express the geometric
mean in terms of product notation:!
!
And this is precisely interesting to me because five-fold geometry does a similar thing. We have
a five-fold expression in our AI equation we arrived at:!
!
In that we take the fifth root of the double integral on left. This makes me thing of how we can
tile a surface with regular polygons the 3-sided (triangle), 4 sided (square), and 6-sided (regular
hexagon) but five pops out and the pentagon requires another shape added in to tile a surface
without leaving gaps as a so-called Archimedean tessellator, the equilateral triangle, square,
and regular hexagon are the regular tessellators. However, if you are working with solids, there
are five regular solids and they all tile to close off a space, using triangles, for example the
tetrahedron, or squares (the cube), and yes the regular pentagon in the dodecahedron.!
See illustration on next page…#
M
0
(x
1
, . . x
n
) =
n
n
∏
i=1
x
i
5
∫
Ge
Si
∫
Ge
Si
∇ ×
u ⋅ d
a =
n
n
∏
i=1
x
i
of 6 18
#
of 7 18
It was the Russian scientist Shubnikov who noticed that five-fold symmetry is more
characteristic of life while six-fold symmetry is more characteristic of the physical. He wrote:!
As to the alive organisms, we have not for them theory, which could answer the question what
kinds of symmetry are compatible or incompatible to existence of living material. But we can
note here that remarkable fact that among the representations of the alive nature the
pentagonal symmetry meets more often.
I think from experience and observation you will find this as true if you pay close attention to
Nature. You will find if you look at flowers every now and then you will find six petals around its
center, or sometimes as with a rose perhaps near a hundred petals, but most often you will find
there are five petals around the center of a flower. As well, even in the rose, with near a
hundred petals, they spiral in as a golden spiral, which is built of ratios of the golden ratio (
and use patterns of Fibonacci numbers. The successive ratios between terms in the Fibonacci
sequence converge on at infinity and the golden ratio is derived from pentagonal symmetry
in that if you draw in the chord of a regular pentagon, the ratio of it to its side is . And indeed
the human has two legs, two arms and a head adding up to five, or two eyes, and a nose and a
mouth adding up to five. Or, five fingers, or five toes on each hand or each foot. But for the
physical like a snowflake, there are six points that form around it giving it hexagonal symmetry.
The starfish has five arms.!
In looking at life we notice it is based on carbon which is in group 14 of the periodic table of
the elements just like semiconductor elements silicon and germanium. It is because of this that
carbon works because it means has 4 valence electrons, meaning it can form long chains with
hydrogen making organic matter the hydrocarbons, utilizing oxygen (O), nitrogen (N),
phosphorus (P), and sulfur (S). Life does not seem to be based on silicon, though, even though
it has 4 valence electrons as well because while carbon can combine with hydrogen to make
hydrocarbons such as CH4, or combine with O, N, H to make the most simple organic
compound isocyanic acid HNCO which binds H-N=C=O, silicon in the presence of oxygen
forms glass SiO2 so easily that it can not combine with the H, N, C, O, P, and S readily with
each equally so as to form functional hydrocarbons.!
It is at this point that I would like to note that carbon is element six in the periodic table giving it
6 protons, and since its molar mass is 12.01, it has 6 neutrons. It so happens that closest
packing of equal radius spheres in the plane like protons, and neutrons is six-around one or
hexagonal symmetry. As Buckminster Fuller constructed his geometry in Synergetics, he
outlined his discovery that equal-radius spheres pack in the form of what he called the vector
equilibrium, which is the cuboctahedron, which he demonstrated was the most transformable
construct and as such becomes pivotal to his Synergetics,!
I would like to suggest in light of this that since carbon has six protons and six electrons, with
the six protons determining its number of electrons (6 to be neutral) giving it four valence
electrons in its outer shell for combining with other elements (the outer shell is four and wants
four to complete an octet, such as four hydrogens each H+, that though life more often meets
with pentagonal symmetry, and here we see carbon meets with six-around-one in the plane, or
twelve-around-one in space as the vector equilibrium, or six-fold symmetry, it is because life is
built out of the physical, like carbon to make the biological, characteristic of pentagonal
symmetry. And it is here I suggest that life animates out of a dynamic structuring of the
physical (inanimate). See illustration on the next page…#
Φ)
Φ
Φ
of 8 18
#
of 9 18
Indeed we see life could be the interplay between 3, 4, 5, 6 as structured in Buckminster
Fuller’s Synergetics. For instance the vector equilibrium (cuboctahedron) is made of equilateral
triangles and squares, the regular tessellators. With eight triangles and six squares. All of this
speaks respectively of NH3 (ammonia, believed to have contributed to making the amino acids
the building blocks of life) which is three hydrogens around a Nitrogen, CH4 (methane, believed
to have contributed to the formation of amino acids in primordial earth as well) the eight
triangles in the cuboctahedron representing the combination of elements such that they
complete an octet, and its six squares, the six protons, six neutrons, and six electrons of
carbon.!
With all said here so far, it might be said that understanding life and its origins can be
understood by looking at artificial intelligence.!
2. The Mathematical Nature of the Means
Let us return to the geometric mean becoming a different function in the f-mean. We have:!
!
!
p=1 yields:!
!
Is the arithmetic mean between x1 and x2. Now take p=-1:!
=!
!
Is the harmonic mean between x1 and x2. Now we try p=0 hoping to get the geometric mean…!
=!
=!
M
f
= f
−1
(
1
n
n
∑
i=1
f (x
i
)
)
M
f
(x
1
, x
2
) = f
−1
(
1
n
2
∑
i=1
x
p
i
)
p
M
f
(x
1
, x
2
) =
(
1
2
x
1
+
1
2
x
2
)
=
x
1
+ x
2
2
M
f
(x
1
, x
2
) =
(
1
2
2
∑
i=1
x
−1
i
)
−1
2
1
x
1
+
1
x
2
=
2x
1
x
2
x
1
+ x
2
M
f
(x
1
, x
2
) =
(
1
2
2
∑
i=1
x
i
0
)
1
0
(
1
2
2
∑
i=1
1
)
1
0
of 10 18
!
So for we can’t make sense and we have to search for a function that will produce
the geometric mean in the f-mean. It is ln(x). This is interesting because the natural log of x was
created to settle the following conundrum:!
!
This is where we need to create the natural logarithm function so we can have a solution to
such an integral and, we have!
!
Where!
!
!
Let us return to our . It is not a sum!
!
But is a product!
=!
!
What this says is that what is important is not the values of data points in an experiment, not
the ’s but the i’s themselves, the number of the data point. Like the one in measurement 1,
the 2 in measurement 2. Never mind that measurement 1 might equal 2.3 grams, measurement
3 might equal 0.5 grams, the important thing is the 1/2 outside the parenthesis because we are
taking, which is is always 1. This is how reality never has any meaning: we
just change to f(x)= ln(x), which is the equivalent of writing!
(
1
2
)
∞
f (x) = x
p
∫
d x
x
=
∫
x
−1
d x =
x
−1+1
0
=
x
0
0
∫
d x
x
= ln(x) + C
ln(x) = log
e
(x)
e = 2.718…
(
1
2
)
∞
1
2
∞
∑
i=1
i
i
=
1
2
(
1
1
+
2
2
+
3
3
+ …
)
M
0
(x
1
, x
2
, x
3
…x
n
) =
1
2
∞
n
∏
i=1
i
i
1
2
(
1
1
⋅
2
2
⋅
3
3
⋅ …
)
x
i
i /i
1/1,2/2,3/3,...
f (x) = x
p
of 11 18
!
Thus it is the experience itself that counts, we find !
!
If we say e=2.718…!
Let us see the derivations and plots…#
G =
n
n
∏
i=1
x
i
∫
d x
x
= ln(x) + C
of 12 18
!
of 13 18
!
of 14 18
!
of 15 18
!
of 16 18
3. Conclusion
While we have the AI BioMatrix!
!
We can form another 3X3 matrix we will call the electronics matrix:!
!
We notice the middle column comprises the most used ductile, malleable, conductive metals
for making electrical wire Cu, Ag, Au,… just like the middle column in the AI BioMatrix contains
C, Si, Ge the semiconductor elements most used in transistor technology Si and Ge and the
core element of biological life C. Grouping the conductors and semiconductors together we
have Si, Ge, Cu, Ag, and Au which make five elements (n=5) which we need to remove the
fifth-root sign in our equation!
!
Thus, we have:!
!
!
=(28.09)(72.64)(12.01)(107.87)(196.97)=!
5
∫
Ge
Si
∫
Ge
Si
∇ ×
u ⋅ d
a =
n
n
∏
i=1
x
i
∫
Ge
Si
∫
Ge
Si
∇ ×
u ⋅ d
a =
5
∏
i=1
x
i
5
∏
i=1
x
i
= Si ⋅ Ge ⋅ Cu ⋅ Ag ⋅ Au
of 17 18
!
Where we have substituted carbon (C=12.01 g/mol) for copper (Cu).!
Taking the fifth root we have 55.375 g/mol which is close to iron (Fe=55.84 g/mol). This is
(55.375)/(55.85)=99% accuracy.!
But since we have:!
!
We take the ratio and have!
!
Almost exactly 3 which is the ratio of the perimeter of regular hexagon to its diameter used to
estimate pi in ancient times by inscribing it in a circle:!
!
Perimeter=6!
Diameter=2!
6/2=3!
!
Thus we have the following equation…!
520680539
r
5
mol
5
∫
Ge
Si
∫
Ge
Si
∇ ×
u ⋅ d
a = 170427030.8(g /m ol )
5
520680539
170427030.8
= 3.055
π = 3.141...
of 18 18
!
Where !
!
!
!
The Author!
π
∫
Ge
Si
∫
Ge
Si
∇ ×
u ⋅ d
a =
5
∏
i=1
x
i
x
1
= C, x
2
= Si, x
3
= Ge, x
4
= Ag, x
5
= Au
∇ ×
u = (Ge ⋅ As − Si ⋅ Ga)
i + (C ⋅ P)
k
d
a =
(
zd ydz
i + yd xdy
k
)
u = (C ⋅ P)
i + (Si ⋅ Ge)z
j + (Ga ⋅ As)y
k
